Higher-Order Semi-Blind Source Separation Approaches Using Canonical Polyadic (CP) Decomposition

Semi-blind source separation (SBSS) approaches are good alternatives to blind source separation (BSS) approaches in applications in which prior knowledge is available about the sources to be extracted. However, their usage has been limited to two-dimensional data sets so far. Therefore, in case of high-dimensional data sets, approaches such as canonical polyadic decomposition (CPD) have been mostly used as a BSS method. The aim of this work is to address this problem by proposing three novel high-dimensional semi-blind source separation methods in the CPD framework. To this end, our first proposed method termed semi-blind alternative least squares (SBALS) is an extension of alternative least squares (ALS), which uses prior knowledge in the separation process. Next, we propose two different versions of the denoising source separation (DSS) framework that can work in a multi-dimensional regime; higher order DSS (HODSS) that extracts sources one by one, and an extension of it termed parallel HODSS (PHODSS) which extracts all the sources simultaneously. We have used both synthesized and real data to evaluate our proposed methods against conventional ALS and DSS methods. Results show that our proposed methods outperform the ALS and DSS methods. More specifically, PHODSS has the best performance among all the considered methods.